Federal Communications Commission (FCC) has allotted a spectrum of bandwidth in the 60 GHz frequency range (57 to 64 GHz). The Wireless Gigabit Alliance (WiGig) is targeting the standardization of this frequency band that will support data transmission rates up to 7 Gbps. Integrated circuits, formed in semiconductor die, offer high frequency operation in this millimeter wavelength range of frequencies. Some of these integrated circuits utilize Complementary Metal Oxide Semiconductor (CMOS), Silicon-Germanium (SiGe) or GaAs (Gallium Arsenide) technology to form the dice in these designs. The receive path of the signal being transferred in the wireless channel in these communication system need to be compensated for various very dispersive conditions occurring in the wireless channel. Some of these conditions include multipath reflection, multipath resilience, ISI (Inter Symbol Interference), channel capacity, strategies for frequency diversity scheduling, etc.
CMOS (Complementary Metal Oxide Semiconductor) is the primary technology used to construct integrated circuits. N-channel devices and P-channel devices (MOS device) are used in this technology which uses fine line technology to consistently reduce the channel length of the MOS devices. Current channel lengths are 40 nm, the power supply of VDD equals 1.2V and the number of layers of metal levels can be 8 or more.
CMOS offers the computing power to perform many of the required compensation techniques requires overcoming the adverse conditions of the wireless channel. Yet, the computing power must be used in a power efficient manner to insure that the dissipated power is low enough to allow these important building blocks of the transceiver fabricated in CMOS to be used in mobile applications. This helps to insure that the energy drawn from the limited power contained in the battery is minimized while achieving the optimum performance.
Orthogonal frequency division multiplexing (OFMA) is a multi-carrier system that has been used in various communication Standards such as 802.11 (Wi-Fi), digital video broadcasting (DVB), asymmetrical digital subscriber lines (ASDL), etc. However, OFDM suffers from several deficiencies including peak to average power ratio (PAPR), sensitivity to amplifier nonlinearities, and effects of frequency offsets. Single carrier (SC) communication systems, however, overcome these several deficiencies and offer several benefits over OFDM systems.
SC communication systems is a single-carrier transmit signal that partitions their wideband channel into a large number of parallel narrowband subcarriers and has a lower PAPR resulting in design parameters in the transmit path that are simpler to achieve when compared to OFDM.
In the transmitter side as illustrated in FIG. 1, the input signals are mapped 1-2 into symbols, then the symbols are converted from a serial path into parallel blocks with a series to parallel (S/P) converter 1-3 so a cyclic prefix 1-4 can be added to each block. A parallel to serial (P/S) converter 1-5 recombines these blocks into a serial link which is zero padded and filtered 1-6. A digital to analog (D/A) converter 1-7 converts the digital serial link to an analog signal and presented to an analog transmitter 1-8. The signal is sent over the wireless channel 1-9 which time disperses the signal and introduces noise 1-21 into the signal. A receiver front end 1-10 receives the distorted wireless signal and converts the signal to a digital signal with an analog to digital (A/D) converter 1-11. The signals are then filtered 1-12. The prefix is removed 1-13 and a S/P converter 1-14 generates a time domain of parallel block signals that are converter by an fast Fourier transform (FFT) 1-15 in to the frequency domain. A frequency domain equalizer 1-16 is applied to each of the transmitted subcarriers where the channel distortion caused by the channel is compensated for each subcarrier by the frequency domain equalizer. The FFT and frequency domain equalization requires less computation power than an equivalent performing time-domain equalization. An inverse FFT (IFFT) 1-17 generates the time domain representation of the frequency compensated transmitted signal to a de-mapper unit 1-18 after which the signal is applied to a P/S converter 1-19. The output signal is applied to the baseband circuitry of the receiver to extract the signals from the transmitter. The composite of the FFT, FDE and IFFT contained within the dotted box 1-20 and will be described in more detail shortly.
In single carrier systems, the operation to create blocks causes latency to increase while bandwidth efficiency is decreased because of the addition of the cyclic prefix which transforms the linear channel convolution into a circular one. However, a block level structure of the signals is required so that the FDE can perform the compensation for each block. The cyclic prefix efficiently eliminates time spreading between the blocks. The time spreading is caused by multi-path propagation of the signal in the wireless channel.
The Discrete Fourier Transform within the FFT (See: T. Widhe, J. Melander, and L. Wanhammar, “Design of Efficient Radix-8 Butterfly PEs for VLSI”, Circuits and Systems, 1997. ISCAS '97. Proceedings of 1997 IEEE International Symposium, 9 Jun. 1997-12 Jun. 1997, pages 2084-2087 vol. 3) is defined as:
                                          X            ⁡                          (              n              )                                =                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                          x                ⁡                                  (                  k                  )                                            ·                              W                nk                                                    ,                  W          =                      ⅇ                                          -                j                            ⁢                                                2                  ⁢                                                                          ⁢                  π                                N                                                                        (                  EQ          .                                          ⁢          1                )            The input is x=[x(0), x(1), . . . , x(N−1)]T while the output is X=[X(0), X(1), . . . , X(N−1)]T. The matrix form X=F8x of the radix-8 Sande-Tukey algorithm can be expressed as:
                              F          s                =                  [                                                    1                                            1                                            1                                            1                                            1                                            1                                            1                                            1                                                                    1                                                              W                  s                                                                              -                  j                                                                                                  -                    j                                    ⁢                                                                          ⁢                                      W                    s                                                                                                -                  1                                                                              -                                      W                    s                                                                              j                                                              j                  ⁢                                                                          ⁢                                      W                    s                                                                                                      1                                                              -                  j                                                                              -                  1                                                            j                                            1                                                              -                  j                                                                              -                  1                                                            j                                                                    1                                                                                  -                    j                                    ⁢                                                                          ⁢                  W                                                            j                                                              W                  s                                                                              -                  1                                                                              j                  ⁢                                                                          ⁢                                      W                    s                                                                                                -                  j                                                                              -                                      W                    s                                                                                                      1                                                              -                  1                                                            1                                                              -                  1                                                            1                                                              -                  1                                                            1                                                              -                  1                                                                                    1                                                              -                                      W                    s                                                                                                -                  j                                                                              j                  ⁢                                                                          ⁢                                      W                    s                                                                                                -                  1                                                                              W                  s                                                            j                                                                                  -                    j                                    ⁢                                                                          ⁢                                      W                    s                                                                                                      1                                            j                                                              -                  1                                                                              -                  j                                                            1                                            j                                                              -                  1                                                                              -                  j                                                                                    1                                                              j                  ⁢                                                                          ⁢                                      W                    s                                                                              j                                                              -                                      W                    s                                                                                                -                  1                                                                                                  -                    j                                    ⁢                                                                          ⁢                                      W                    s                                                                                                -                  j                                                                              W                  s                                                              ]                                    (                  EQ          .                                          ⁢          2                )            and after the matrix is factored:
                              F          s                =                              [                                                            1                                                  0                                                  0                                                  0                                                  1                                                  0                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  1                                                  0                                                  0                                                  0                                                                      -                    j                                                                                                0                                                  1                                                  0                                                  0                                                  0                                                  j                                                  0                                                  0                                                                              0                                                  0                                                  1                                                  0                                                  0                                                  0                                                  1                                                  0                                                                              1                                                  0                                                  0                                                  0                                                                      -                    1                                                                    0                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  1                                                  0                                                  0                                                  0                                                  j                                                                              0                                                  1                                                  0                                                  0                                                  0                                                                      -                    j                                                                    0                                                  0                                                                              0                                                  0                                                  1                                                  0                                                  0                                                  0                                                                      -                    1                                                                    0                                                      ]                    ⁢                                                                 [                                                                            1                                                              0                                                              0                                                              0                                                              1                                                              0                                                              0                                                              0                                                                                                  1                                                              0                                                              0                                                              0                                                                                      -                        1                                                                                    0                                                              0                                                              0                                                                                                  0                                                              1                                                              0                                                              0                                                              0                                                              j                                                              0                                                              0                                                                                                  0                                                              1                                                              0                                                              0                                                              0                                                                                      -                        j                                                                                    0                                                              0                                                                                                  0                                                              0                                                              1                                                              0                                                              0                                                              0                                                              1                                                              0                                                                                                  0                                                              0                                                                                      -                        1                                                                                    0                                                              0                                                              0                                                              1                                                              0                                                                                                  0                                                              0                                                              0                                                                                                                -                          j                                                ⁢                                                                                                  ⁢                                                  W                          s                                                                                                            0                                                              0                                                              0                                                                                      W                        s                                                                                                                        0                                                              0                                                              0                                                                                      j                        ⁢                                                                                                  ⁢                                                  W                          s                                                                                                            0                                                              0                                                              0                                                                                      -                                                  W                          s                                                                                                                    ]                            ⁢                                                                 [                                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                                            1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                            0                                                                    0                                                                    0                                                                                                            0                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                                                            0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                            0                                                                    0                                                                                                            0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                    0                                                                                                            0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                            0                                                                                                            0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                                                            0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                                      ]                                                                                        (                  EQ          .                                          ⁢          3                )            where the signal flow graph of the radix-8 butterfly is illustrated in FIG. 2A. This butterfly uses 24 complex additions 2-1, 2 multiplications by
                              F          8                =                              [                                                            1                                                  0                                                  0                                                  0                                                  1                                                  0                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  1                                                  0                                                  0                                                  0                                                                      -                    j                                                                                                0                                                  1                                                  0                                                  0                                                  0                                                  j                                                  0                                                  0                                                                              0                                                  0                                                  1                                                  0                                                  0                                                  0                                                  1                                                  0                                                                              1                                                  0                                                  0                                                  0                                                                      -                    1                                                                    0                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  1                                                  0                                                  0                                                  0                                                  j                                                                              0                                                  1                                                  0                                                  0                                                  0                                                                      -                    j                                                                    0                                                  0                                                                              0                                                  0                                                  1                                                  0                                                  0                                                  0                                                                      -                    1                                                                    0                                                      ]                    ⁢                                                                 [                                                                            1                                                              0                                                              0                                                              0                                                              1                                                              0                                                              0                                                              0                                                                                                  1                                                              0                                                              0                                                              0                                                                                      -                        1                                                                                    0                                                              0                                                              0                                                                                                  0                                                              1                                                              0                                                              0                                                              0                                                              j                                                              0                                                              0                                                                                                  0                                                              1                                                              0                                                              0                                                              0                                                                                      -                        j                                                                                    0                                                              0                                                                                                  0                                                              0                                                              1                                                              0                                                              0                                                              0                                                              1                                                              0                                                                                                  0                                                              0                                                                                      -                        1                                                                                    0                                                              0                                                              0                                                              1                                                              0                                                                                                  0                                                              0                                                              0                                                                                                                -                          j                                                ⁢                                                                                                  ⁢                                                  W                          8                                                                                                            0                                                              0                                                              0                                                                                      W                        8                                                                                                                        0                                                              0                                                              0                                                                                      j                        ⁢                                                                                                  ⁢                                                  W                          8                                                                                                            0                                                              0                                                              0                                                                                      -                                                  W                          8                                                                                                                    ]                            ⁢                                                                 [                                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                                            1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                            0                                                                    0                                                                    0                                                                                                            0                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                                                            0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                            0                                                                    0                                                                                                            0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                    0                                                                                                            0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                            0                                                                                                            0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                    1                                                                                                            0                                                                    0                                                                    0                                                                    1                                                                    0                                                                    0                                                                    0                                                                                              -                          1                                                                                                      ]                                                                                        (                  EQ          .                                          ⁢          3                )            2-2, and 4 trivial multiplications by j 2-3. The three stages of the butterfly are shown as 2-1, 2-4 and 2-5.
For a 512 FFT operation, FIG. 2B presents a table 2-6 where the total complex multiplications, real multiplications, complex additions, real additions and the number of memory accesses for an FFT using Radix-2 2-7, Radix-4 2-8 and Radix-8 2-9. The multiplications are the most complicated operations. Note that for the Radix-8 case, the number of complex multiplications is only 896, while the real multiplications increase to 768. Note that four multiplications are required for the complex multiplications. Thus, the overall multiplications of the Radix-8 are about 1150 which is about 25% less overall multiplications than the Radix-4 case. In addition, the memory access is about 40% less that the Radix-4 case.
FIG. 3A presented the block diagram of an architecture for a pipelined FFT processor using a radix-r butterfly. The input signal is applied to an unscrambler 3-1 to generate r inputs to the first Radix-r Butterfly processing unit (PE) 3-2. A first commutator 3-3 re-routes the output signals of the first Radix-r Butterfly PE 3-2 to the second Radix-r Butterfly PE 3-4. Similarly, the second commutator 3-5 re-routes the output signals of the second Radix-r Butterfly PE 3-4 to the third Radix-r Butterfly PE 3-6 to generate the final output signals.
In FIG. 3B, another representation of the architecture for a radix-8 is illustrated. The input signal is applied to a first S1 buffer 3-8 to generate 8 inputs to the first S1 Radix-8 Butterfly processing unit (PE) 3-9. The S1 twiddle factors 3-7 are also applied to the first PE 3-9. The twiddle factor refers to a complex multiplication of a constant to allow recursively combining smaller FFTs. An S2 buffer 3-10 captures and applies the output signals of the first S1 Radix-8 Butterfly PE 3-9 to the second S2 Radix-8 Butterfly PE 3-11. The S2 twiddle factors 3-12 are also applied to the second PE 3-11. Similarly, third S3 buffer 3-13 captures and applies the output signals of the second S2 Radix-8 Butterfly PE 3-11 to the final Radix-8 Butterfly PE 3-14 with a twiddle factor of 1 to generate the final output signals.
The dotted box 1-20 in FIG. 1 is expanded in FIG. 4 to provide a block diagram of the frequency domain equalizer (FDE). This block diagram is used to determine the transfer equations for the FTT 4-1, equalizer 4-4 and IFFT 4-5. The FDE supports binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK). The system operates on a block of 8 complex samples every cycle for 64 cycles performing at a rate of 440 MHz/512 points. The FFT 4-1 and IFFT 4-5 can be radix-8 butterflies (the IFFT uses conjugate inputs) while the equalizer 4-4 is a multiplier. A time domain signal y(t) is applied to the input of the FFT-512. In addition, the time domain signal h(t) of the channel estimation is also applied to the FFT-512. The FFT-512 generates a frequency signal H(f) which is applied to the H(f) buffer 4-3. The output of the H(f) buffer 4-3 generates:
                                          H            ^                    ⁡                      (            f            )                          =                              H            ⁡                          (              f              )                                                                                                            H                  ⁡                                      (                    f                    )                                                                              2                        +                          σ              2                                                          (                  EQ          .                                          ⁢          4                )            which is applied to the equalizer 4-4 where σ is the noise in the channel. The frequency transformed signal Y(f) at the output of the FFT-512 is also applied to the equalizer. The signal at the output of the equalizer is {circumflex over (X)}(f) and is given by:
                                          X            ^                    ⁡                      (            f            )                          =                                                                              H                  ⁡                                      (                    f                    )                                                  *                            ⁢                              Y                ⁡                                  (                  f                  )                                                                                                                                            H                    ⁡                                          (                      f                      )                                                                                        2                            +                              σ                2                                              =                                                                      H                  ^                                ⁡                                  (                  f                  )                                            *                        ⁢                          Y              ⁡                              (                f                )                                                                        (                  EQ          .                                          ⁢          5                )            The signal {circumflex over (X)}(f) is applied to the IFFT-512 4-5 to generate the estimated output signal {circumflex over (x)}(t).
The time domain channel estimate ĥ(n) is used to calculate
                                          H            ^                    ⁡                      (            k            )                          =                              1            N                    ⁢                                    ∑                              n                =                0                                            N                -                1                                      ⁢                                                            h                  ^                                ⁡                                  (                  n                  )                                            ⁢                              ⅇ                                                      -                    j                                    ⁢                                                            2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      kn                                        N                                                                                                          (                  EQ          .                                          ⁢          6                )            and Parseval′ theorem
                                          ∑                          n              =              0                                      N              -              1                                ⁢                                                                                    h                  ^                                ⁡                                  (                  n                  )                                                                    2                          =                              1            N                    ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                                                                                H                    ^                                    ⁡                                      (                    k                    )                                                                              2                                                          (                  EQ          .                                          ⁢          7                )            is used to calculate the estimated signal to noise ratio (SNR).
                              Estimated          ⁢                                          ⁢          S          ⁢                                          ⁢          N          ⁢                                          ⁢          R                =                                            ∑                              n                =                0                                            N                -                1                                      ⁢                                                                                                h                    ^                                    ⁡                                      (                    n                    )                                                                              2                                            σ            2                                              (                  EQ          .                                          ⁢          8                )            The SNR is used to determine the Error Vector Magnitude (EVM) for the Minimum Mean Square Error (MMSE) Frequency Domain Estimator (FDE):
                              Estimated          ⁢                                          ⁢          E          ⁢                                          ⁢          V          ⁢                                          ⁢          M                =                                            σ              2                        N                    ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                          1                                                                                                                                      H                        ^                                            ⁡                                              (                        k                        )                                                                                                  2                                +                                  σ                  2                                                                                        (                  EQ          .                                          ⁢          9                )            If after the header is decoded, the estimated EMV is not sufficient to decode the packet, then the packet is ignored to save power.
The SC FDE can perfectly equalize for multipath using a 64-tap delay line. The operation of the FDE requires Interference and Noise power estimation. The FFT and IFFT operation occurs for each transmission block. The modulation scheme can be binary phase switch keying (BFSK) or quandary phase switch keying (QPSK). The SNR for the FFT and IFFT is about 30 db.
More detail of the FFT-Equalizer-IFFT path is depicted in FIG. 5. A control unit 5-6 provides the control signals for the datapath flow. The input signals of the datapath 5-2 are applied to the Storage block 5-4. The output of the Storage block 5-4 is provided to the MUX 5-5. The channel estimation uses the Golay Matched Filter 5-1 to generate the channel estimation 5-3 of the wireless channel and is also provide to the MUX 5-5. A digital signal (not illustrated) selects one of the two inputs to the MUX. Eight streams are applied to the FDE where a symbol consisting of a plurality of bits is sampled each clock tick. These signals are sent to the FFT-512 4-1 which transforms the time domain signals to the frequency domain signals. The FFT-512 4-1 generates a frequency signal H(f) which is applied to the H(t) buffer 4-3. The output of the H(f) buffer 4-3 is applied to the equalizer 4-4. The IFFT-512 4-5 transforms the frequency domain signals of the datapath back to the time domain where the signals are compensated by the CPE Comp 5-7. The time domain signals at the output of the IFFT-512 are also used to estimate the common phase error (CPE) 5-8 which is then applied to the CPE Comp. The final signals are applied to the QAM demapper 5-9 and applied to the baseband signal processing elements (not illustrated).